Mike is referring to me. I've owned a Traveler for 9 years, and a Tiger for 2 months, but I've been involved with Grumman's longer than that, as part of my private pilot training was in a Cheetah. I will be unashamedly biased towards the Grumman line. I can't really give you much comparison between a Grumman and a Cherokee/Arrow, as I've only flown a PA28 once (and it was a 1960's dog of a lease-back plane).
If you haven't already, find someone who will give you an introductory ride in both (hint, hint), to see which model you like better. Talk to them, pick their brains, find out the things that can be particular gotcha's about them. Get on their user forums (request access to the Grumman one at
grumman-gang@mailman.xmission.com) Get a thorough prebuy from someone that knows the aircraft well, and isn't associated with the airplane. If you decide on a Tiger, get a pre-buy at the best Grumman guru shop you can find. They are not as well known as other aircraft and things can get missed by the average shop that can be real gotchas. I can help you find good shops around the country, and the 'guru's' are scattered around the US as well.
Feel free to contact me off-forum and we can talk more, if Grumman is what you are looking for (and you know you are, look at the swinging pocket-watch, its telling you, Grumman, Grumman, Grumman.........)