The Winchester Model 1907 differs from an assault rifle in using a much heavier and more powerful round: the .351 Winchester Self-Loading bullet alone weighs 12 g, about the same as the weight of an entire 5.56×45mm NATO cartridge (11-13 g for the full cartridge, 4 g or less for the bullet). So within whatever your weight limit is for carrying around ammunition, you can carry about three times as many rounds for an AR15 as you can for the 1907 (which is the whole point of an assault rifle). Further, the AR15 will have a faster accurate fire rate due to much lower recoil and noise.
Even leaving fully automatic fire aside, the much lower ammo load you can carry and the slower accurate fire rate makes the 1907 in no way functionally equivalent to a modern assault rifle for military purposes.
But if your purpose is shooting up a school or shopping mall the case isn't so clear cut. A slightly slower fire rate isn't such a big problem when you have little need to suppress combatants firing back at you and lower accuracy at a given fire rate is also a lesser problem when the range at which you're firing is much lower than in typical military encounters. The much heavier .351 round will transfer significantly more kinetic energy to the target, but there is extensive argument over how much difference this really makes terms of stopping power and lethality, particularly with regard to the 5.56 round and it's associated AR15 rifle.
The exact goals of those shooting a large number of civilians are unclear to me (to put it mildly), so it's very hard to judge whether those wanting to do a mass shooting would consider the Winchester Model 1907 to be functionally equivalent to an AR15 for their purposes. There are quite a number of factors involved, and these may even include how people feel about the look of the weapon itself and how the shooter feels they will be perceived when using one weapon versus the other. It is indisputable that using an assault rifle will allow you to carry a lot more ammunition and, generally, give you a slightly higher fire rate; certainly it's conceivable that this will allow a shooter to more effectively achieve his goals.
Even assuming that the 1907 is functionally equivalent to an AR15 for a mass shooter's goals, the availability of the 1907 a century ago is not evidence that "[t]he semi-auto can be safely owned by civilians" now, as Leah Rosson claims, just that it was apparently safely owned then. And even that might be disputed (at least by the victims) if it were used in, for example, lynchings, which were considerably more common in the U.S. back then than they are now.
The safety of civilians owning firearms seems to be heavily dependent on the particular country and society one is talking about. Plenty of folks in favour of minimal firearm ownership regulation are fond of pointing to other countries with high rates of firearm ownership which see hugely lower rates of mass shootings, though that sounds to me like an argument that Americans are thus more in need of regulation of firearm ownership than other countries. I note also that the reasons Rosson claims for the increase in mass shootings (mainly, less liberalism and more religion and conservatism) are more widespread in other countries that experience far fewer mass shootings.
(In case people are wondering about my views, I consider collecting and/or shooting firearms to be a perfectly valid hobby that, like any other hobby, shouldn't be restricted unless that's necessary to achieve other important societal aims. (I don't find gun-related hobbies interesting to me personally, however, unless you consider first-person-shooter games to be "gun-related.") I also think that there may well be forms of restriction that could be significantly effective at reducing mass shootings yet not be any more restrictive than regulations we already have for things like automobiles. But I live far from the U.S. in a country nearly without mass shootings so the whole problem is more an intellectual curiosity to me than something that will affect me personally in any way.)
