Unfortunately, you don't get to make the choice. When an app decides to use Steemconnect as their login tool, then they also decide which level of permission they want to request.

So in this case, if they want your active key, I'd be asking the developer why they need that level of access to my account.

Now, if you use Steemconnect directly to take some kind of action on your account and are not prompted by an app or website, for example, undelegating Steem Power, then it's probably fine, but if an app is using Steemconnect to ask you for permanent permissions, then I'd think really hard about giving anything more than my posting key.

Basically, if you're giving an app your active key, do so realizing that you could easily wake up to find that all your liquid Steem and SBD is gone and only your Steem Power will remain.

If you're ok with that risk, then that's when you'd hand over your active key.

Under no circumstances would I ever hand out my owner key, and I treat my active key in much the same way.