<p>In <a href="https://3dprinting.stackexchange.com/a/3116/37">this question</a> I was told that I should use silver solder to connect the heating element to the power supply.</p>

<p>(I was also told that a ceramic extruder head was the way to go, but I'm working with what I have)</p>

<p>I bought two types of silver solider from Radio Shack: </p>

<ul>
<li>96/4 Silver-Bearing Solder, Lead-Free 0.62" diameter.</li>
<li>62/36/2 Silver-Bearing Solder, 0.15" diameter.</li>
</ul>

<p>Is there any reason I should use one of these over the other to power the heading element of the J-Head extruder?</p>

The first is not suitable. ASTM96TS Sn96Ag4 has a melting point of 221–229 °C according to
Wikipedia
. Pb96Ag4 would be OK, but that is not lead free so doesn't seem to match your description.
Update from comment to explain the letters and numbers: the data comes from wikipedia, the numbers are Tin(Sn) 62%, Pb(Lead) 36%, Ag(Silver) 2%, for example, see below for an electronics solder compound
.
Sn62Pb36Ag2 is an ordinary expensive electronics solder (but not lead free), with an even lower melting point.
You need to find a high temperature silver solder, with a melting point of about 305 °C (which confusingly might be a soft silver solder), for example one of
these
. Hard silver solders melt at 600 °C, that would be excessive in this application.
The nomenclature 'silver solder' came about before lead-free electronics solder was introduced, since when more alloys containing silver have become popular as general purpose solders.