Let's first look at the Opening Crawl:
THE FORCE AWAKENS
Luke Skywalker has vanished. In his absence, the sinister FIRST ORDER has risen from the ashes of the Empire and will not rest until Skywalker, the last Jedi, has been destroyed.
With the support of the REPUBLIC, General Leia Organa leads a brave RESISTANCE. She is desperate to find her brother Luke and gain his help in restoring peace and justice to the galaxy.
Leia has sent her most daring pilot on a secret mission to Jakku, where an old ally has discovered a clue to Luke’s whereabouts…
"From the ashes" is our first clue. The Empire has fallen. Past tense.
The second is the rebel insignia itself - it's an abstraction that is quite reminiscent of the Jedi Order insignia during the Clone Wars: An elongated star arising between wings displayed sans bird.
The Resistance is, judging from the persons present, and the insignias, both rank and squadron, essentially New Republic Detached Forces. This has a number of historical precedents in the real world. The US has generated several such "volunteer groups" over the years... the most famous being the American Volunteer Group, under Gen. Chennault, which fought in China against the Japanese more than a year before the US officially joined the war. Likewise, the "Polish Air Force" was a mixture of US and UK citizens, Polish refugees, and some cadre and planes that escaped German bombing, which served the "Polish Government in Exile." The AVG, or Flying Tigers, used US uniforms, but without the usual patches. The PAF used Polish uniform patterns manufactured in the UK (when they bothered to wear uniforms, according to a former member). The PAF and the Flying Tigers both retained the insignia of their parent services for the duration of their "irregular status" during WW II.
The Resistance has the same kind of look as the AVG: uniforms with slightly differentiated insignia, the same symbols of allegiance, and same rank structures and equipment. (The Resistance uses bars on the rank plate, where the Rebellion used dots... but it really does look like they just "connected the dots".)
Meanwhile, looking to some of the chatter about the current canon novels, it generally seems that the Empire as a whole fell (just like in the SWEU), and like the SWEU, it appears several portions of the Empire continued to exist after the New Republic. Some of which apparently sued for peace with the New Republic.
Snoke's stated goals, as elucidated by his mouthpiece officer, General Hux, include conquering not just the New Republic, but also the other Former Imperials. Since they are, essentially, at war with the rest of the galaxy, having unique insignia is of utility. It's a practical matter to keep themselves from identifying with "lesser remnants"...
We can see that the First Order is strong; surprisingly so given the hype about it being a remnant. It's professional. It needs a logo for both morale and intimidation value. The old Imperial logo lacks a certain credibility... both with fans ("You got beaten by a bunch of Teddy Bears") and the residents of the Galaxy ("You no longer have clear superiority"). It also is quite likely that the other remnants of the Empire are reverted to somewhat less militaristic states.
Also, there is historical use to think about... Many a nation has fallen, and/or split... The Bosnians, Serbians, and Croatians continue to use the Uniforms and Equipment of Yugoslavia... but use different national symbols. Likewise, the Russian Federation uniforms are much like the Soviet ones - same ranks, same insignia of grade, but the double eagle replaces the hammer and sickle, and RFR replaces SSSR. Japanese Self Defense Forces uniforms are not much different from the Imperial Japanese Navy uniforms.
So, essentially, The First Order needs to distinguish between themselves and other "Imperial Remnants" for both political and practical reasons, and wants to retain compatibility with extant gear (and possibly gear captured from other remnants). The Resistance wants to show it's ties to the New Republic for propaganda reasons, and makes minimal changes so as to not break the treaties with other factions of the old Empire.
Now, out-of-universe, it is a marketing ploy. All the really cool toys are First Order... because we only see the T-70A X-Wing II for the Resistance, but we see the Landers, Ties, at least one other starcraft... And by different branding, there's less confusion for the end purchase over who the good guys are (by retaining a familiar symbol), and more freedom to play the "Impies vs Firsties" with your collection of figures and toys.