I've finished both on hard with no deaths, so it's definitely do-able.
Path of Radiance on hard with no deaths isn't really a major issue. You shouldn't have too much trouble with that. Play defensively, and your resets should be in the 1-digit amount.
Radiant Dawn is a whole other situation. Part 1 isn't a lot harder than on normal, as your enemies won't crit you a lot. Part 2 can be a bit of a pain. 2-f and the one were Geoffrey is your lord are going to be your two main issues. On 2-f, just sit uber-defensive and don't bother using the royal guard. On the Geoffrey as lord one, either let your allies just run in and die, or have them sit in defensive.
Part 3 is a pain. It's going to be harder than part 4. Your enemies have a high critrate and you're going to have a lot of characters who cannot survive a crit. Expect to have a reset a chapter at least here.
Part 4 isn't actually that hard. It's back to a part 2 difficulty. Your only real issue is the one where you recruit Tormod. I just ended up holing myself up in one of the rooms with a treasure chest, with Ike and someone else swapping turns on guarding the door.
It's a hell of a lot of fun, and it's mighty hard. Remember to stick to using characters with high def and high health. Mages are also incredibly valuable, both for their staves and for the fact that they're going to be your hardest hitters (save the Laguz royals) by the end of the game. Speedy low-damage classes with low def(like Myrmidons) are going to be rather useless. I used Mia because I like the character, but she never really did a lot.
As for Meg vs Zihark. Meg wins by a long shot. If you manage to level her up, that is. It's a lot of work to start off with, but I'd say it's worth it. The Dawn Brigade really needs characters with def in part 3.
Zihark can't survive a crit from anything. That makes him pretty much completely useless by part 3, as mostly everyone has a small percentage chance to crit him, even with his luck. Using Zihark is fine in easy/normal, but he's downright bad at hard.
Scottie, I have no idea where you get the idea that Zihark has a lot more avoid than Meg at level 20/20/20. Meg's at 94% and Zihark is at 105%. Sure, there's a difference, but it doesn't make up for the def and res differences.
Essentially, Zihark wins on offence, but he's still not going to be a damage dealer. Zihark doesn't do any job well, whereas Meg's at least a good defensive character.
