If you are using smaller sized text then Verdana would be the better choice between these two as it's much easier to read at the smaller sizes. If you are not using small text sizes then you can use whichever you like the looks of best.
I think both of them look good on the screen, and to my eyes seriously doesn't make a big difference to use any of them on the web; but I must say I've been a fan of Times all my life, it looks really good once is printed. Now, I think it also depends on how comfy you feel when you read those fonts, and in that case I would keep Verdana, it has clean lines and you can read it even at a very small size. Tahoma gives more the Windows look, so in case you need it for something specific and Windows related, this one will do.
In my opinion, Verdana looks better than Tahoma, but seriously is not like a huge difference, as long as they are good for reading, and they give a nice presentation, that will be just fine for me.
Honestly, both of those fonts look aesthetic enough for pretty much any website.
Up until now, I've only used Verdana, I had to search up Tahoma in order to compare them, bus still... I prefer Verdana, it's just become a standard nowadays.