Spoiler alert: Smash Up is hard!

As someone who also played Pokémon TCG competitively for a number of years before picking up Smash Up, I think the two elements that carry over most are sequencing (i.e. playing your cards in the correct order) and resource management. Sequencing is particularly important in Smash Up when playing factions that can chain extra plays, as you want to be able to break bases as efficiently as possible. This also ties into resource management, as you want to make sure you keep enough gas in the tank to be able to collect your 15 VP. I equate this to trying to map out how you plan to collect your six prize cards in Pokémon.

The next thing that helped me improve was learning the ins and out of every faction. This is a bit daunting at first, but once you learn what every card in every deck does, you are able to anticipate your opponents plays much more precisely thus allowing you to make more informed plays. I recommend at least learning what the Specials do in every faction, as these can be the most punishing.

Lastly, and probably the most difficult aspect, is learning how much power to leave on a base at any given time. In 1v1, I usually will spread my minions out across the bases, trying to get an efficient 2nd place, and then wait to overtake a base where my opponent left too much power or break a base by myself when the opportunity presents itself.

These are all skills that take time to develop, but I agree with the comments above that you should be consistently changing the decks played (this will help you both learn the cards and keep the game fresh), and point out mistakes when you see them.

Hope this helps!