Very interesting thread. Simply stated, both Chris and Tracy felt threatened by each other, albeit in different ways. Certainly Tracy in her own way attempted to create some distance in disassociating herself from Chris's image. She was in the process of forming her own identity, and recognized right away that being categorized as a mere Chrissie-clone by the press was far from complimentary. She wanted to be recognized for her own achievements and style, and evidently found it necessary to deny any role- model associations with Chris and thus, indirectly, deny her any credit for influencing her game. Certainly however, Chris was an influence, yet there were significant distinctions in both their games (and as noted) personalities as well. Chris in general played a more fluid on-court style, whereas IMO, Austin's game came off as a bit mechanical. Though Chris's serve was generally not viewed as a weapon, it could still be quite effective when she was on, particularly her use of placement. Conversely, Austin's serve was clearly a liability, though because her groundstrokes were so strong, she was often able to recover from an opponents deep returns.
Concerning groudstrokes, Austin in general hit with slightly more pace, whereas Evert tended to utilize more variety...Austin hit flatter, whereas Evert utilized slight topspin, sidespin and flat strokes in general. This, I believe, is more an influence of the fact that Chris was raised on clay courts, and Tracy on cement. Unfortunately for Austin, this also likely contributed to her later injuries, as clay is a far more forgiving surface on the body in ones formative years than is cement.
Evert also used finesse more in her game, which when she was on, compensated well with Austin's power groundies. Evert's overhead was also a stronger shot than Austin's, which to quote writer Peter Bodo, when Austin went to hit the shot it "always looked like an adventure."
I have personally only viewed two Evert-Austin matches: their '79 and '80 US Open struggles. What I recall most about the '79 match is that Austin simply went for broke, hit out on every shot and was fiercely detirmined to win every point. Although Chris had beaten Tracy in the tournament prior, she clearly felt a ton of pressure to win this particular match and hence, a fifth consecutive Open title. Chris's faulty strategy IMO is that she did not give Tracy any change of pace and instead attempted to outslug Austin from the baseline, hitting harder and harder as the match wore on (and thus made more errors) which wasn't really her style. In short, she was reduced to playing Austin's game, which was an obvious losing strategy. A year later in the semi-finals, Chris simply played smarter, well thought out and intelligently constructed tennis. At 0-4 in the first set, their 1980 match simply seemed a continuation from the year prior. Then almost immediately, a lightbulb seemed to go off in Chris's head; suddenly Evert started throwing in a wide variety of dropshots (and lobs if successfully retrieved), off-pace strokes, and in general, successfully pushed Austin around the court. Evert played clever, inspiring, imaginative tennis, winning 16 of the next 20 games. Whereas in the '79 match, Chris generally seemed to play scared and didn't have much of a game plan (she later stated she wrongly assumed Austin would be nervous playing her first Slam final), the following year she played with genuine confidence and grit, stating she was "prepared to stay out there all day" if necessary, to win.
Lastly, concerning their personal attitudes towards one another, Austin at times seemed rather intimidated by Chris's image and overall popularity. In her autobiography, Austin labels Chris's look as "ultra-feminine," which to me strikes closer to personal insecurity than anything of real accuracy (Chris never looked like a wannabe drag queen, ok?!). While Tracy was considered cute by many, during this period Chris was outright sexy. Even my gay friends can't deny this! Although she in no way played it up to the extent of a Kournakova, neither did she try to hide this "side" of her, and the fans (at least her fans) loved her for it. Concerning Tracy, I too wish her career had not been so cruelly halted by fate* (in a sense, similiar to Little Mo); I cheered her comeback attempts and was glad to see her beat one of the Maleva's in her last go at it. I also enjoyed her battles with Pam Shriver (as well as Martina), admitedly loving it when Pam actually cussed her out on court at net after a match. Those two had a great rivalry and from what I recall, Tracy didn't have Pam's number the way Chris did, which I think their closeness in age, and therefore, the pressure being more on Austin, played a role in it, as well as Pam's general familiarity with Tracy's game from way back in the juniors.
*And the chance for Chris to improve upon her 8-9 career match deficit!