I often know what's coming but I cannot seem to stop it.

Over the last few months I've been playing someone who has me questioning things just a little. I love players that make me think. Now we're pretty close in level; both in the 1500s. He was below me but since he's won the majority of our games, he's climbed some.

Often I know exactly what he's going to do, what he's thinking, and where he's trying to go. Yet, no matter what, his moves seem perfect. I just can't quite manage stop his plan. Every piece is arranged in such a way that I have no viable counter play.

I'm well aware of piece utilization. A lot of players focus on one piece, usually the queen. I don't. I generally have several pieces focused on a task or backing a play. Still, he seems to do this better than I can. Even so, our games normally even, material-wise, and close out with a pawn race.

I would just like to be able to see the solutions to his tactics. 

Has anyone else had this sort of issue with a player who was so close in skill level?

Having no counter play isn't a tactical issue, it's a strategic issue.

Sounds like he knows what the opening aims for (for his side). Sounds like you do too (for his side). What you need to know is what kind of play the opening gives your side in return.  Only a few openings (impractical ones) offer only the prospect of direct defense. This sort of play is passive and avoided by pros (and generally anyone who knows what they're doing). Defense is fine, but passivity is not.

As an easy example, in the french defense, advanced variation, white seeks play on the kingside, because that's where his main pawn chain affords him extra space. Black counters in the center (against the d and e pawns) and on the queenside.

This is often how it is: when your opponent has play in one area of the board (kingside, center, or queenside) your job is to stir up trouble in one of the other areas.

When you undermine their pawn structure (especially in the center) and create threats, then their ability to attack (or otherwise seek play in their area) is diminished. After you've done this, you can go for some direct defense of course, but solely using passive defense is usually a recipe for disaster.

As for knowing what your opponent is aiming for, that will happen more and more often as you improve, because it's not their intentions that count, it's what the position itself is offering to each player.

It would help if you showed an example of one of your games with this player so that we can analyze it and see what strategic, tactical, and positional changes you could have implemented to avoid losing the position. 

I personally find this sort of rivalry to be very beneficial to my chess. The frustration you feel when losing to a player within your grasp can be enough to make the next push in your chess improvement. 

"Tactics flow from a superior position." -Bobby Fischer.

It's hard without seeing specific positions, but based on your description, I have one very strong suspicion - your opponent seems to understand the concept of tempo better than you do.  If you're always responding to what the opponent does, you aren't taking any time to set up your attack.  Against a player like that, the best option is not always to defend, but more often to figure out how to attack faster yourself!

As it so happens, I had exactly that problem against an attacking Expert (2000 rating) at my local club not long ago.  The answer was not more precise defense of better prophylaxis, it was to attack faster.  I never pulled even with him, mind you, but I went from scoring 0% to scoring about 25% within a few months, which is no small improvement.  Knowing what attack is coming doesn't mean you can stop it, but knowing that your attack will strike home first does.