Comparing Two Algorithms for 3SUM problem over Integers The paper "Subquadratic Algorithms for 3SUM", by Ilya Baran, Erik D. Demaine, Mihai Patrascu has the following complexity for the 

3SUM problem: given a list $L$ of $n$ integers if there are $x,y,z \in L$ such that $x+y=z.$

They state, "On a standard word RAM with $w-$bit words, we obtain a running time of 
$O(n^2/ \max\{w \log w, \log n (\log \log n)^2 \})$. In the circuit RAM with one nonstandard $AC0$ operation, we obtain $O(n^2/ w^2 \log w)$. In external memory, we achieve $O(n^2/(MB))$, even under the standard assumption of data indivisibility. Cache-obliviously, we obtain a running time of $O(n^2/ MB \log M )$. In all cases, our speedup is almost quadratic in the “parallelism” the model can aﬀord, which may be the best possible. See the Baran, Demaine, Patrascu paper here.

Recently, a paper "Threesomes, Degenerates, and Love Triangles" by Grondlund and Pettie has proved that "the decision tree complexity of 3SUM is $O(n^{3/2}\sqrt{\log n})$,  and that there is a randomized 3SUM algorithm running in $O(n^2(\log \log n)^2/\log n)$ time, and a deterministic algorithm running in $O(n^2(\log \log n)^{5/3}/(\log n)^{2/3})$ time. 

These results refute the strongest version of the 3SUM conjecture, namely that its decision tree (and algorithmic) complexity is $Ω(n^2)$." 

See this second paper here.

Clearly, both are important papers. Not being an expert to this area, my question is about how to compare the impact and significance of either, given the different complexity models. Any other insightful comments about this problem is also welcome. For example had the first paper already ruled out the $\Omega(n^2)$ bound?
The first paper essentially gives a subquadratic algorithm if we know that every input number has $w$ bits and we can add two $w$ bit numbers in one step. This was not a very surprising result and it did not rule out an $\Omega(n^2)$ bound.

The second paper does not use any such assumptions and improves the exponent of $n$ for decision trees, which is a surprise, although not as big as it would be for all algorithms, for which they have only improved slightly (thus disproving the strongest conjecture). I would guess that more results will follow shortly.