Primo de Rivera was much different from Franco in some aspects: unlike Franco, Primo's fascism was very similar to early italian fascism. It was republican, antitraditionalist and modernist; and despite its strong catholic influence, it would be much less conservative than Franco's Spain. In this sense, Primo was very similar to, say, Italo Balbo. Compare this with francoist Spain, which was an absolute monarchy in all but name, and where the most insanely ultraconservative and reactionary wings of conservatism and carlism held power until the late 50's. In fact, from the 40's onward, a surprising number of falangists actively opposed Franco, after seeing that he had betrayed their revolution. Some of them, such as Dionisio Ridruejo, evolved from Falange leaders in the 30's and 40's to pro-democracy demonstrators in the 60's.
Falangism (in theory) also opposed the big capital. AFAIK, it is the only fascist group I know that actively incorporated sindicalism into its doctrine. Franco kept that, but without any ideological load. That is the main difference between francoism and falangism to be taken into account: falangism is an ideology, and it actively seeked to change spanish society following the fascist way. Francoism is not an ideology, it is in fact an anti-ideolgical system. Franco always was a soldier, not a politician: he ruled Spain for 40 years as if it was a military barracks, and, with the idea that spaniards were tired of politics, tried to keep the entire country in stasis, until he relaxed his grip in the 60's. There are plenty of friction points between Franco and Primo de Rivera if Primo survives. Franco wanted nothing short of absolute power, because he thought that was the only way to prevent Spain from collapsing, and god forbid anything like an actual change in spanish society, even towards fascism. However, by the end of the war, Falange's power had waned, and all actual power was in the army. I think that either there could have been a shorter civil war in the early 40's -maybe with god knows what effects in WWII- or, most likely, Primo would have been quietly disposed for.
There are, in fact, many conspiracy theories about Franco refusing to help Primo because he knew he would be more useful dead than alive.