I haven't found the sponsored tweets annoying at all. I mostly don't even notice them. I scan my feed and I only pay attention to the tweets which interest me. Everything else could be an ad as far as I'm concerned.

The number of sponsored ads don't seem high enough to make me feel like it's annoying.

As for Twitter clients. Eh, not sure I care so much. I just need a decent client which doesn't suck.

I think their recent decision sort of suck but as a user I don't know that I care too much.