Mario is much greater to pop culture and Nintendo's survival. A lot of mainline Mario games are easier to understand than Zelda games.
Personally, I prefer Mario even if only comparing mainline Mario games to mainline Zelda games. I get into them more and I don't think there are 3 Zelda games on the quality of the Galaxy games and Odyssey (though Ocarina of Time is close and Breath of the Wild is pretty close too).

Overall, both series in their totality, is what I meant, just to clarify.

Mario, and it's not even close!!

Zelda only broke the 20-million mark with *BotW*; before that, most games didn't even reach 10 million!

Mario should be compared to Pokémon; Zelda doesn't even come close in terms of popularity, fame, or status as a pop-culture icon.

In terms of quality? Very tricky...

To organize my thoughts, I'm going to go through the two series, platform by platform, and compare contemporary entries.

• NES - Both series have a revolutionary debut followed by a "black sheep" successor. The difference is the Super Mario Bros 3 provided a larger and more refined version of the original's formula, whereas, Zelda wouldn't get something similar until the SNES. (Winner: Super Mario)
• GB - Super Mario Land has aged badly, but SML2 is very solid. However, I think Link's Awakening takes the edge here. And it appears Nintendo agrees, seeing how they thought the game was a solid basis for a full budget game in 2019. (Winner: Legend of Zelda)
• SNES - I'm not going to say Super Mario World and Link to the Past are anything but equal. (Winner: Tie)
• N64 - Super Mario 64 was more revolutionary and important, but I find Ocarina of Time more fun to actually go back to. Maybe it's because SM64's controls compare unfavorably to newer entries, whereas Legend of Zelda puts more of an emphasis on dungeon design than controlling Link? Also, Majora's Mask. (Winner: Legend of Zelda)
• GBC - Link's Awakening DX + Oracle Duology is better than an NES port with screen crunch, extra features or not. (Winner: Legend of Zelda)
• GBA - The Super Mario Advance series is a stronger overall package than the Zelda games on GBA, but it's hard to give Mario credit when Zelda was the only one not relying on ports. It helps that Four Swords and Minish Cap are fun experiences in their own right. (Winner: Legend of Zelda)
• GC - I haven't played through all of Super Mario Sunshine, but I doubt that it would beat the GameCube LoZ games. Wind Waker and Twilight Princess are beloved for a reason. (Winner: Legend of Zelda)
• DS - This is a relative weak point for both series, but I think NSMB is better than either Phantom Hourglass or Spirit Tracks. (Winner: Super Mario)
• Wii - Skyward Sword is not considered the best Zelda, and Twilight Princess only gets some credit as a port. Meanwhile, the Galaxy duo are considered some of the best 3D platformers ever made, and NSMB Wii was a step up from the already-good DS outing. (Winner: Super Mario)
• 3DS - This console's Super Mario games feel a bit like worse versions of Wii U games that were released shortly afterwards, and that have since gotten better versions on Switch. Even ignoring the two very solid N64 remakes, Link Between Worlds was the best 2D Zelda in 20 years. Triforce Heroes... came out. (Winner: Legend of Zelda)
• Wii U - For Mario, we had the fourth NSMB game in six years and 3D World. For Zelda, we had two solid HD remakes and the version of Breath of the Wild hardly anybody played. I would give this to Legend of Zelda on the back of Breath of the Wild, except I've heard the game runs a bit worse on Wii U, and haven't played that version. And 3D World is possibly my favorite 3D platformer ever. (Winner: Tie)
• NS - I don't really know how to judge this. Breath of the Wild is one of the best games ever, but it's technically a Wii U port. Super Mario Odyssey and Tears of the Kingdom are both great but disappointing games. Bowser's Fury was a great experience, but wasn't a full title. Super Mario Bros Wonder was the best 2D Mario this century, but I don't think it was quite top tier. And I haven't played Echoes of Widsom yet. (Winner: Tie)

Total Score: Super Mario wins 3 times, Legend of Zelda wins 5 times, and we have 3 ties.

I guess that means I prefer Legend of Zelda.

As a mass market IP? Mario
As a game IP? Zelda

• NES: The Legend of Zelda is superior to Super Mario Bros., but Super Mario Bros. 3 tops them all [Mario wins]
• GB: I think Link's Awakening is slightly better than Super Mario Land 2, the best of the Super Mario Land sub-series, but it's three games versus one [Tie]
• SNES: A Link to the Past and Super Mario World are essentially equals. The margin is razor thin. However, if you count Yoshi's Island as a part of the Yoshi series and the Super Mario series and (which I do), then Super Mario takes the win [Mario wins]
• N64: Having recently replayed both Super Mario 64 and Ocarina of Time, I firmly believe SM64 is the superior game. However, I'd argue Ocarina + Majora's Mask matches the brilliance of SM64 [Tie]
• GBC: this isn't close, even if the Oracle games aren't the peak of the Zelda series. Super Mario Bros. Deluxe just isn't essential [Zelda wins]
• GBA: More ports from Super Mario, more new games from Zelda. Minish Cap remains a great adventure [Zelda wins]
• GCN: the weakest 3D Super Mario versus one of the best of the entire Zelda series in Wind Waker [Zelda wins]
• DS: this is similar to the N64 match-up. I think New Super Mario Bros. is the best individual game, but it's two games versus one. And Spirit Tracks, in my mind, is the single most underrated game in the Zelda franchise [Tie]
• Wii: I love Twilight Princess, but Skyward Sword is relatively weak. Meanwhile, Super Mario Galaxy and its sequel are two of the best games ever made. Plus New Super Mario Bros. Wii [Mario wins]
• 3DS: A Link Between Worlds is a masterpiece. The Mario games simply can't compete [Zelda wins]
• WiiU: New Super Mario Bros. U is the best of that sub-series and Super Mario 3D World is one of the top Super Mario games ever. Plus Super Mario Maker. Since I'm pushing Breath of the Wild to NS...[Mario wins]
• NS: this one is tight. Super Mario Odyssey + Bowser's Fury + Wonder + Super Mario Maker 2 vs. Breath of the Wild + Tears of the Kingdom + Echoes of Wisdom. I think the greatness of the BotW/TotK duology is just enough to emerge victorious [Zelda wins]

So, that's five wins for Zelda and four wins for Super Mario. I acknowledge this isn't the perfect way to arrive at a conclusion, since some wins are bigger and more meaningful than others. If, instead, we go by my top 50 list, I have seven Super Mario games and seven Zelda games. That shows a closer contest. For me, these two franchises really are 1a and 1b. However, since Breath of the Wild is my #1 game, I will use that as the tiebreaker. Zelda is the victor.

I have a lot of trouble picking one tbh, but ultimately I think Mario is just that bit more consistently great; while I love Zelda titles like Ocarina, BOTW, TOTK, Twilight Princess, A Link to the Past, Skyward Sword, etc, I really didn't like Wind Waker or Majora's Mask, while the only Mario I felt kinda fell flat was Sunshine.

Still, both absolutely elite series that both boast some of the greatest games ever made.

Are we talking about an objective analysis—taking into account popularity, sales history, market presence, cultural impact, and other numerical and determinable criterias demonstrating that "X" is more significant and "bigger" than "Y"?

Or is it simply a personal opinion based on "I prefer this game series ( because... )"?

Objectively, Zelda doesn't compare to Mario—not even close. The difference in scale and significance is absolutely colossal! Mario is one of the three most iconic video game franchises of all time! Zelda, on the other hand, barely cracks the Top 10 (if it even makes the list at all). Breath of the Wild was the first Zelda game to break the 20-million-unit mark—a figure that is routine for Mario and other major franchises.

Edit:

Personal opinion. I also pick Mario, many Mario games are timeless classics. Only very feel Zelda games, like "A Link to the past", "Link's awakening" and " A Link between words " truly are timeless.

Which you feel is better subjectively, not in terms of sales/etc.