This thread kind of got a little off track. Here's my two cents to the question in the header.
The bullshark is the P35 in new pants. The P35 is basically the evolution of the P15. Now, what I don't know is if the P35 air cylinder is titanium. The P15's is claimed to be titanium and that's why it is so light. Titanium air cylinder aside, they are well designed guns. The barrel on the .25 is a little thin and you have to be careful with the pressure you put on the set screws, but they are awesome little light guns. In my opinion, having used both the original Avenger and the P15, I think that the Avenger is certainly more versatile, but not built as well, as the P15. So it comes down to what you want, versatility or compactness.
You didn't ask about the Avenge X, but a lot of people have thrown it in this conversation, and it really shouldn't be. It, is the evolution of the Avenger, and is just plain better, and even more versatile than the original, and it's cost reflects that. I think for a beginner that wants to learn about all levels of tuning, and future versatility, the Avenge X would be the one to get though. At this point, with the X being available, I wouldn't have the original. However, if you don't want to do anything but go out and shoot, have fun for the least dollars spent, the Bullshark. The bullpup design and compactness makes it so much easier to bring places and use. And even with that, you could get an Avenge X bullpup too, if you wanted to spend the extra money.
If you really like airgunning, with whatever you choose, you will be buying more.