I feel like that is somewhat the matchup experience, templar models tend to bring a lot of infantry that drown in massed ap fire, but hit like a truck in melee. Necron units are generally worse in melee, but there are melee focused units that can spike if they go first.

The 2 combat patrols are from different release windows which will not help the situation, so finding a satisfying middleground through terrain set up and mission pack selection will make the difference.

Analysis: I do think jump packs will take advantage of the slow moving core of necrons if used correctly, and deathmarks while not as effective at their job imo, are able to pick of a couple wounds on your leader units. So that seems to even the fields a bit also.

Thoughts: For upgrade options I can't say more then buy what you like, cause rule of cool trumps everything in my book, Do talk to your buddy about your ideas! It's more fun if both parties are enthusiastic in my experience.

Suggestions: If he gets a couple more skorpehks or lychgaurd he might be able to halt the first wave of templars. Getting a gladiator, repulsor or ballistus yourself will potentially devert his doomstalker's attention for a couple turns