In terms of:

1) Hardware Sales

2) Profit

3) Software Sales

Well WiiU is a home console so comparing profit and software sales is a tad unfair. After all handhelds naturally sell a lot less software and Nintendo makes all their profit on those 1st party game sales. Just look at the top 10 selling games of each and its obvious how far ahead Nintendo are in these catagories. Hardware sales... well they are rather even but WiiU will pull ahead in the end by a few million imo.

Hardware sales, profit and software sales are quite easily in the Wii U's favor.

All 3 are in Wii U's favor.

Wii U: almost 43 million games sold at retail
PSV: almost 35 games sold at retail

Wii U: plenty of profit for nintendo, small to almost no profit for anyone else
PSV: small to almost no profit for Sony and anyone else

Wii U will most probably surpass the PSV in hardware sales some day (but it's not guaranteed).

1) Wii U
2) Wii U
3) Wii U

Do people know the Vita's profitability, or that of its memory card sales?

Vita is also a largely a digital console, Its retail software sales are not a fair picture? More then half of its games are digital exclusive.

What is clear is that Nintendo are making a lot of money off the software they sell on Wii U

The Vita gets tonnes of support, devs wouldn't keep giving it if it wasn't worth their time.

1) Wii U
2) Both (!!!)
3) PS Vita (Digital sales are huge and bigger than Retail sales!!!)

What is more profitable for third party developers? WiiU or PSVita?

The number of released and (even more important) announced third party games for both systems should be a hint.