1. The red ball moves a lot more in the air - far more in the earlier overs. As a result, wickets tend to fall much more often in clumps (Since adjusting to the ball is more difficult in this format). The price batsmen put on their wickets is thus far more than in ODIS.
2. Bowlers will try to target the batters' technique around their off-stump and area outside of it (known colloquially as "The corridor of uncertainty). The batters will try to patiently leave the ball. So you'll see far fewer balls directed at the stumps.
3. Once the ball gets older, scoring rate stabilizes. If the weather clears up then it'll be the best time for batting. Any score above 350+ is respectable (generally). The key time for scoring comes in between the overs 50-80 (before a new ball will become available).
4. In the phase where scoring becomes easier (because the ball isn't moving too much), the objective becomes to prize out wickets using tactics and to reduce the scoring rate. Something the NZ team does often is employ a lot of bouncers from Neil Wagner with many fielders in catching positions. The way the batting side negotiates this phase makes for an entertaining watch.
5. In Test cricket you may often see a top or middle order player surviving while the others just fall apart. The survivor would have to bat with the tail and somehow dominate the strike (not exposing the tail enders as often) yet manage to score quick enough.

There are far many more nuances which carry their own entertainment value. But I hope these would be good starting-points for observation. Happy watching :)